Problem: Solve for $x$ and $y$ using elimination. ${x-2y = 1}$ ${-x+5y = 2}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $3y = 3$ $\dfrac{3y}{{3}} = \dfrac{3}{{3}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x-2y = 1}\thinspace$ to find $x$ ${x - 2}{(1)}{= 1}$ $x-2 = 1$ $x-2{+2} = 1{+2}$ ${x = 3}$ You can also plug ${y = 1}$ into $\thinspace {-x+5y = 2}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(1)}{= 2}$ ${x = 3}$